Results 261 to 270 of about 29,061 (317)

Inverse and Ill-Posed Problems $$\star $$

2018
When we evaluate the expression \({{\varvec{f}}} = A{{\varvec{u}}}\), where \({{\varvec{u}}}\) and \({{\varvec{f}}}\) are vectors and A is a matrix, we solve a direct or forward problem. Given A we can precisely calculate \({{\varvec{f}}}\) for any \({{\varvec{u}}}\).
Simon Širca, Martin Horvat
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Ill-posed problems

1987
This section is devoted to a preliminary discussion of the stability problem. We shall give a definition of ill-posed problems and sketch the main idea to restore stability in ill-
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Regularization of Discrete Ill-Posed Problems

BIT Numerical Mathematics, 2004
Discrete approximations \( A_n u_n = f_n \) of an ill-posed equation (1) \( Au = f \) with a linear compact operator \( A: X \to X \) in a Hilbert space \( X \) are considered. Here, \( A_n: X_n \to X_n \) is a linear bounded operator in a finite-dimensional Hilbert space \( X_n \), where \( \{X_n,r_n,p_n\} \) is a convergent and stable discrete ...
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Ill-Posed Problems

1983
Problems involving differential equations usually come in the following form: we are given an equation for the unknown function u, P(u) = f, on a domain Ω together with some “side” conditions on u. For example, we may require that u assumes certain preassigned values on ∂Ω, or that u is in L 2(Ω), or that u is in class C k in Ω.
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On a Monotone Ill–posed Problem

Acta Mathematica Sinica, English Series, 2005
Let \(X\) be a real reflexive Banach space with dual \(X^*\). Let \(A:X \rightarrow X^*\) be a nonlinear continuous monotone operator. In general, the equation \(Ax=f, \;f\in R(A)\), is ill-posed, i.e., its solutions do not depend continuously on \(f\).
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Ill-Posed Problem Instances

1993
This chapter consists of those sections of a longer work [5] which formed the basis for much of the author’s talk at the Smalefest. The longer work contains complete proofs and develops much additional material.
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Spectroscopy; An Ill-Posed Problem

SPIE Proceedings, 1985
Spectroscopy can be described as an inversion technique for the retrieval from measured data of an unknown spectral distribution. The implications which follow from this general approach are discussed. It turns out that spectroscopy belongs to the category of ill-posed problems that have more degrees of freedom than data.
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Ill-Posed Problems of Geomechanics

Физико-технические проблемы разработки полезных ископаемых, 2018
The classical solution of elasticity problem on deformation of a plane weakened by a mathematical cut under wedging by constant forces is analyzed. The ill-posedness of the classical failure mechanics statements for problems with angular points is demonstrated.
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Ill-posed problems in mechanics

Mechanics of Solids, 2016
The notion of ill-posed initial and boundary value problems for partial differential equations was introduced by Hadamard, who also presented the first example of an ill-posed problem for a specific partial differential equation. At the same time, there are numerous examples of ill-posed problems in any field of mechanics.
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Ill-Posed Problems and Regularization

1998
Click on the DOI link to access the article (may not be free). ; In this chapter, we consider the equation.
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